The Reynolds Averaged Navier-Stokes (RANS) models are still the workhorse in current engineering applications due to its high efficiency and robustness. However, the closure coefficients of RANS turbulence models are determined by model builders according to some simple fundamental flows, and the suggested values may not be applicable to complex flows, especially supersonic jet interaction flow. In this work, the Bayesian method is employed to recalibrate the closure coefficients of Spalart-Allmaras (SA) turbulence model to improve its performance in supersonic jet interaction problem and quantify the uncertainty of wall pressure and separation length. The embedded model error approach is applied to the Bayesian uncertainty analysis. Firstly, the total Sobol index is calculated by non-intrusive polynomial chaos method to represent the sensitivity of wall pressure and separation length to model parameters. Then, the pressure data and the separation length are respectively served as calibration data to get the posterior uncertainty of model parameters and Quantities of Interests (QoIs). The results show that the relative error of the wall pressure predicted by the SA turbulence model can be reduced from 14.99% to 2.95% through effective Bayesian parameter estimation. Besides, the calibration effects of four likelihood functions are systematically evaluated. The posterior uncertainties of wall pressure and separation length estimated by different likelihood functions are significantly discrepant, and the Maximum a Posteriori (MAP) values of parameters inferred by all functions show better performance than the nominal values. Finally, the closure coefficients are also estimated at different jet total pressures. The similar posterior distributions of model parameters are obtained in different cases, and the MAP values of parameters calibrated in one case are also applicable to other cases.

Roughness-induced transition control is a key technology for aircraft design, and associated research is useful in practical applications as well as for understanding the mechanism of the roughness-induced transition. One practical approach involves the “shielding effect,” whereby the roughness-induced transition is shielded by smaller pockets of surrounding roughness. In this paper, we investigate the shielding effect of a two-dimensional downstream strip in the boundary layer disturbed by discrete smooth-edged roughness and focus on the shielding strip height k_ss and the distance between the two areas of roughness x_ss. Our results indicate that downstream shielding delays the transition by weakening the strongest streamwise vortices in the middle of the wake, thus inhibiting the “lift-up” effect that induces growth in the disturbance. The main mechanisms for reducing the streamwise vorticity are (a) enhanced dissipation of the streamwise vorticity and (b) conversion of streamwise vorticity into more stable spanwise vorticity. The strip suppresses the separation zone behind the roughness, thus affecting the receptivity process and reducing the initial disturbance. However, the strip strengthens other streamwise vortices in the wake. When k_ss exceeds a critical value, vortices closer to the wall will induce stronger lift-up than those in the middle of the wake, resulting in an earlier transition. Analysis of x_ss shows a simpler trend, whereby the onset position of the transition moves upstream as x_ss increases. This is because the shielding strip weakens the streamwise vortices earlier and the separation zone becomes smaller as the strip moves closer to the discrete roughness patch.

Turbulence modeling based on the Reynolds-averaged Navier–Stokes (RANS) method has been widely applied in industry, but its performance in some complex flows is far from satisfactory. The improvement of turbulence models based on the traditional framework has not made breakthrough progress for decades. In this study, a data-driven turbulence modeling framework based on the reconstruction of Reynolds stress discrepancies is used to aid in the improvement of turbulence models, with the Reynolds stresses of the shear-stress transport model being modified in the eigenspace. The large eddy simulation (LES) dataset of a set of bump cases is used to provide high-fidelity information on adverse-pressure-gradient flows for the modeling framework. First, the Reynolds stress tensors of RANS and LES are compared in terms of amplitude, shape, and orientation. Then, the random forest (RF) algorithm is employed to map the mean flow features to the Reynolds stress discrepancies. The well-trained RF model greatly improves the predictions of Reynolds stresses and other flow variables for the attachment and separation states and enables the numerical simulations to have predictive accuracy close to LES and computation time of the same order of magnitude as RANS.